Calculating sample sizes for cluster randomized trials: we can keep it simple and efficient!

J Clin Epidemiol. 2012 Nov;65(11):1212-8. doi: 10.1016/j.jclinepi.2012.06.002.


Objective: Simple guidelines for calculating efficient sample sizes in cluster randomized trials with unknown intraclass correlation (ICC) and varying cluster sizes.

Methods: A simple equation is given for the optimal number of clusters and sample size per cluster. Here, optimal means maximizing power for a given budget or minimizing total cost for a given power. The problems of cluster size variation and specification of the ICC of the outcome are solved in a simple yet efficient way.

Results: The optimal number of clusters goes up, and the optimal sample size per cluster goes down as the ICC goes up or as the cluster-to-person cost ratio goes down. The available budget, desired power, and effect size only affect the number of clusters and not the sample size per cluster, which is between 7 and 70 for a wide range of cost ratios and ICCs. Power loss because of cluster size variation is compensated by sampling 10% more clusters. The optimal design for the ICC halfway the range of realistic ICC values is a good choice for the first stage of a two-stage design. The second stage is needed only if the first stage shows the ICC to be higher than assumed.

Conclusion: Efficient sample sizes for cluster randomized trials are easily computed, provided the cost per cluster and cost per person are specified.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Budgets
  • Cluster Analysis*
  • Data Interpretation, Statistical*
  • Guidelines as Topic
  • Humans
  • Randomized Controlled Trials as Topic / economics
  • Randomized Controlled Trials as Topic / statistics & numerical data*
  • Sample Size*